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Multidimensional stable laws G α admit a well-known Lévy–LePage series representation G α = L ∞ j=1 Γ −1/α j We present (asym-ptotically) optimal bounds for the total variation distance between a stable law and the distribution of a partial sum of the Lévy–LePage series. In the one-dimensional case similar results were obtained earlier by Bentkus, Götze and(More)
In this paper we analyze Cantor type sets constructed by the removal of open intervals whose lengths are the terms of the p-sequence, {k −p } ∞ k=1. We prove that these Cantor sets are s-sets, by providing sharp estimates of their Hausdorff measure and dimension. Sets of similar structure arise when studying the set of extremal points of the boundaries of(More)
The standard normal distribution on R d satisses ?? @C " 6 c d ", for all " > 0 and for all convex subsets C R d , with a constant c d which depends on the dimension d only. Here @C denotes the boundary of C, and ? @C " stands for the "-neighborhood of @C. Such bounds for the normal measure of convex shells are extensively used to estimate the accuracy of(More)
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